Finite Group Databasebeta

← C13×#14028 #15700367

Subgroups — C13×#14028 #15700367

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C211yesmaximal, characteristic, complemented
2C2×C13×#385C211yesmaximal, characteristic
3C2×C13×#380C211yesmaximal, characteristic
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
5C22×C13×#95C211yesmaximal, characteristic
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1443C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1434C211yesmaximal, characteristic, complemented
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C13×#387—24no—
30C13×#385—24no—
31C13×#380C418yescomplemented
32C4×C13×C22⋊C4—24no—
33C2×C13×#95—24no—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13—41no—
74C23×C4×C13—41no—
75C23×C4×C13—41no—
76C23×C4×C13C2×C414yes—
77C23×C4×C13Q814yes—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4C2×C414yescomplemented
103C2×C13×C4⋊C4C2×C414yescomplemented
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4C2×C414yes—
114C2×C13×C22⋊C4C2×C414yes—
115C2×C13×C22⋊C4D414yes—
116C2×C42×C13—22no—
117C2×C42×C13—22no—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
120C2×C42×C13—41no—
121C2×C42×C13—41no—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95—41no—
141C13×#95C2×C414yescomplemented
142C13×#95C2×C414yescomplemented
143C13×#95D414yes—
144#14028C1311yesmaximal, characteristic, direct product factor, Sylow
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13C22×C412yes—
154C24×C13C2×D412yes—
155C24×C13C2×Q812yes—
156C24×C13#4112yes—
157C24×C13#4112yes—
158C24×C13#4112yes—
159C24×C13#4112yes—
160C24×C13C2411yescharacteristic
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—28no—
170C22×C4×C13—28no—
171C22×C4×C13—28no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—28no—
233C22×C4×C13—28no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—44no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13—44no—
252C22×C4×C13—44no—
253C22×C4×C13—44no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×C13—44no—
261C22×C4×C13—44no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13C22×C412yes—
265C22×C4×C13C22×C412yes—
266C22×C4×C13C22×C412yes—
267C22×C4×C13C22×C412yes—
268C22×C4×C13C22×C412yes—
269C22×C4×C13C22×C412yes—
270C22×C4×C13C2×D412yes—
271C22×C4×C13C2×D412yes—
272C22×C4×C13C2×D412yes—
273C22×C4×C13C2×D412yes—
274C22×C4×C13C2×D412yes—
275C22×C4×C13C2×Q812yes—
276C22×C4×C13C2×Q812yes—
277C22×C4×C13#4112yes—
278C22×C4×C13#4112yes—
279C22×C4×C13#4112yes—
280C13×C4⋊C4—28no—
281C13×C4⋊C4—44no—
282C13×C4⋊C4—44no—
283C13×C4⋊C4—44no—
284C13×C22⋊C4—28no—
285C13×C22⋊C4—28no—
286C13×C22⋊C4—28no—
287C13×C22⋊C4—44no—
288C42×C13—44no—
289C42×C13—44no—
290C2×#387C2×C1311yescharacteristic, complemented
291C2×#385C2×C1311yescharacteristic
292C2×#380C2×C1311yescharacteristic
293C2×C4×C22⋊C4C2×C1311yescharacteristic
294C22×#95C2×C1311yescharacteristic
295#1445C2×C1311yescharacteristic, complemented
296#1443C2×C1311yescharacteristic, complemented
297#1442C2×C1311yescharacteristic, complemented
298#1441C2×C1311yescharacteristic, complemented
299#1436C2×C1311yescharacteristic, complemented
300#1436C2×C1311yescharacteristic, complemented
301#1434C2×C1311yescharacteristic, complemented
302C22⋊#95C2×C1311yescharacteristic
303C22⋊#95C2×C1311yescharacteristic
304C22⋊#95C2×C1311yescharacteristic
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13#11714yes—
334C23×C13C4×D414yes—
335C23×C13C4×Q814yes—
336C23×C13C22⋊Q814yes—
337C23×C13#12314yes—
338C23×C13#12514yes—
339C23×C13#12614yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×Q811yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
354C23×C132−1+411yescharacteristic
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—416no—
398C2×C4×C13—416no—
399C2×C4×C13—416no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13C4×D414yes—
455C2×C4×C13C22⋊Q814yes—
456C24×C4C22×C1311yescharacteristic
457C24×C4C22×C1311yescharacteristic
458C24×C4C22×C1311yescharacteristic
459C22×C4⋊C4C22×C1311yescharacteristic
460C22×C4⋊C4C22×C1311yescharacteristic
461C22×C4⋊C4C22×C1311yescharacteristic
462C22×C4⋊C4C22×C1311yescharacteristic
463C22×C22⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465C22×C22⋊C4C22×C1311yescharacteristic
466C22×C22⋊C4C22×C1311yescharacteristic
467C22×C42C22×C1311yescharacteristic
468C22×C42C22×C1311yescharacteristic
469#387—24no—
470#385—24no—
471#380C4×C1318yescomplemented
472C4×C22⋊C4—24no—
473C2×#95—24no—
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C2×#95C22×C1311yescharacteristic
482C2×#95C22×C1311yescharacteristic
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
494C2×#95C22×C1311yescharacteristic
495C2×#95C22×C1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—24no—
500C22×C13—24no—
501C22×C13—24no—
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—24no—
506C22×C13—24no—
507C22×C13—24no—
508C22×C13—24no—
509C22×C13—24no—
510C22×C13#38718yescomplemented
511C22×C13C2×#11711yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13C2×C4×Q811yescharacteristic
515C22×C13C4×#4111yescharacteristic
516C22×C13#51811yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13C2×C22⋊Q811yescharacteristic
519C22×C13C2×C22⋊Q811yescharacteristic
520C22×C13C2×#12311yescharacteristic
521C22×C13#52511yescharacteristic
522C22×C13C2×#12511yescharacteristic
523C22×C13C2×#12611yescharacteristic
524C22×C13#52911yescharacteristic
525C22×C13#53311yescharacteristic
526C22×C13#53811yescharacteristic
527C22×C13#53911yescharacteristic
528C22×C13#54311yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13#54611yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54611yescharacteristic
534C22×C13#54611yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13#55111yescharacteristic
538C22×C13#55111yescharacteristic
539C22×C13#55111yescharacteristic
540C22×C13#55111yescharacteristic
541C22×C13#55211yescharacteristic
542C22×C13#55211yescharacteristic
543C22×C13#55311yescharacteristic
544C22×C13#55311yescharacteristic
545C22×C13#55311yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552C4×C13—42no—
553C4×C13—42no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—42no—
558C4×C13—81no—
559C4×C13—81no—
560C25C23×C1311yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—41no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4—41no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4C2×C4×C1314yes—
581C23×C4Q8×C1314yes—
582C23×C4C23×C1311yescharacteristic
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C23×C4C23×C1311yescharacteristic
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C23×C4C23×C1311yescharacteristic
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C2×C4×C1314yescomplemented
607C2×C4⋊C4C2×C4×C1314yescomplemented
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4C2×C4×C1314yes—
618C2×C22⋊C4C2×C4×C1314yes—
619C2×C22⋊C4D4×C1314yes—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—41no—
625C2×C42—41no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—41no—
640#95—41no—
641#95—41no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95C2×C4×C1314yescomplemented
646#95C2×C4×C1314yescomplemented
647#95D4×C1314yes—
648C2×C13—28no—
649C2×C13C2×#38711yescharacteristic
650C2×C13C4×C22⋊Q811yescharacteristic
651C2×C13#232911yescharacteristic
652C2×C13#234211yescharacteristic
653C2×C13#234311yescharacteristic
654C2×C13#236111yescharacteristic
655C2×C13#236411yescharacteristic
656C2×C13#241811yescharacteristic
657C2×C13#241911yescharacteristic
658C2×C13#243711yescharacteristic
659C2×C13#243811yescharacteristic
660C2×C13#244211yescharacteristic
661C2×C13#248111yescharacteristic
662C2×C13#251011yescharacteristic
663C2×C13#256911yescharacteristic
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C22×C4×C1312yes—
673C24C2×D4×C1312yes—
674C24C2×Q8×C1312yes—
675C24C13×#4112yes—
676C24C13×#4112yes—
677C24C13×#4112yes—
678C24C13×#4112yes—
679C24C24×C1311yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4C22×C4×C1312yes—
784C22×C4C22×C4×C1312yes—
785C22×C4C22×C4×C1312yes—
786C22×C4C22×C4×C1312yes—
787C22×C4C22×C4×C1312yes—
788C22×C4C22×C4×C1312yes—
789C22×C4C2×D4×C1312yes—
790C22×C4C2×D4×C1312yes—
791C22×C4C2×D4×C1312yes—
792C22×C4C2×D4×C1312yes—
793C22×C4C2×D4×C1312yes—
794C22×C4C2×Q8×C1312yes—
795C22×C4C2×Q8×C1312yes—
796C22×C4C13×#4112yes—
797C22×C4C13×#4112yes—
798C22×C4C13×#4112yes—
799C4⋊C4—28no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C42—44no—
808C42—44no—
809C13#1402811yescharacteristic, direct product factor, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23C13×#11714yes—
839C23C4×D4×C1314yes—
840C23C4×Q8×C1314yes—
841C23C13×C22⋊Q814yes—
842C23C13×#12314yes—
843C23C13×#12514yes—
844C23C13×#12614yes—
845C23C23×C4×C1311yescharacteristic
846C23C22×D4×C1311yescharacteristic
847C23C22×D4×C1311yescharacteristic
848C23C22×Q8×C1311yescharacteristic
849C23C2×C13×#4111yescharacteristic
850C23C2×C13×#4111yescharacteristic
851C23C2×C13×#4111yescharacteristic
852C23C2×C13×#4111yescharacteristic
853C23C2×C13×#4111yescharacteristic
854C23C2×C13×#4111yescharacteristic
855C23C2×C13×#4111yescharacteristic
856C23C13×H(5,𝔽2)11yescharacteristic
857C23C13×H(5,𝔽2)11yescharacteristic
858C23C13×H(5,𝔽2)11yescharacteristic
859C23C13×2−1+411yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—416no—
903C2×C4—416no—
904C2×C4—416no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4C4×D4×C1314yes—
960C2×C4C13×C22⋊Q814yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22C13×#38718yescomplemented
976C22C2×C13×#11711yescharacteristic
977C22C2×C4×D4×C1311yescharacteristic
978C22C2×C4×D4×C1311yescharacteristic
979C22C2×C4×Q8×C1311yescharacteristic
980C22C4×C13×#4111yescharacteristic
981C22C13×#51811yescharacteristic
982C22C13×#52011yescharacteristic
983C22C2×C13×C22⋊Q811yescharacteristic
984C22C2×C13×C22⋊Q811yescharacteristic
985C22C2×C13×#12311yescharacteristic
986C22C13×#52511yescharacteristic
987C22C2×C13×#12511yescharacteristic
988C22C2×C13×#12611yescharacteristic
989C22C13×#52911yescharacteristic
990C22C13×#53311yescharacteristic
991C22C13×#53811yescharacteristic
992C22C13×#53911yescharacteristic
993C22C13×#54311yescharacteristic
994C22C13×#54411yescharacteristic
995C22D42×C1311yescharacteristic
996C22C13×#54611yescharacteristic
997C22C13×#54611yescharacteristic
998C22C13×#54611yescharacteristic
999C22C13×#54611yescharacteristic
1000C22C13×#54711yescharacteristic
1001C22C13×#54811yescharacteristic
1002C22C13×#55111yescharacteristic
1003C22C13×#55111yescharacteristic
1004C22C13×#55111yescharacteristic
1005C22C13×#55111yescharacteristic
1006C22C13×#55211yescharacteristic
1007C22C13×#55211yescharacteristic
1008C22C13×#55311yescharacteristic
1009C22C13×#55311yescharacteristic
1010C22C13×#55311yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C2—28no—
1026C2C2×C13×#38711yescharacteristic
1027C2C4×C13×C22⋊Q811yescharacteristic
1028C2C13×#232911yescharacteristic
1029C2C13×#234211yescharacteristic
1030C2C13×#234311yescharacteristic
1031C2C13×#236111yescharacteristic
1032C2C13×#236411yescharacteristic
1033C2C13×#241811yescharacteristic
1034C2C13×#241911yescharacteristic
1035C2C13×#243711yescharacteristic
1036C2C13×#243811yescharacteristic
1037C2C13×#244211yescharacteristic
1038C2C13×#248111yescharacteristic
1039C2C13×#251011yescharacteristic
1040C2C13×#256911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#387C2semidirect
6. C13×#1445C2semidirect
7. C13×#1443C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
10. C13×#1436C2semidirect
11. C13×#1436C2semidirect
12. C13×#1434C2semidirect
31. C13×#380C4semidirect
102. C2×C13×C4⋊C4C2×C4semidirect
103. C2×C13×C4⋊C4C2×C4semidirect
141. C13×#95C2×C4semidirect
142. C13×#95C2×C4semidirect
144. #14028C13direct (N × H)
290. C2×#387C2×C13semidirect
295. #1445C2×C13semidirect
296. #1443C2×C13semidirect
297. #1442C2×C13semidirect
298. #1441C2×C13semidirect
299. #1436C2×C13semidirect
300. #1436C2×C13semidirect
301. #1434C2×C13semidirect
471. #380C4×C13semidirect
510. C22×C13#387semidirect
606. C2×C4⋊C4C2×C4×C13semidirect
607. C2×C4⋊C4C2×C4×C13semidirect
645. #95C2×C4×C13semidirect
646. #95C2×C4×C13semidirect
809. C13#14028direct (N × H)
975. C22C13×#387semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C13×#3872
C2×C13×#3852
C2×C13×#3802
C2×C4×C13×C22⋊C42
C22×C13×#952
C13×#14452
C13×#14432
C13×#14422
C13×#14412
C13×#14362
C13×#14342
C13×C22⋊#952
#1402813